Tag Archives: chemistry

We’ve talked a lot about the different chemical elements and the periodic table, so I loved finding the infographic below which shows the natural abundance of those elements in the universe, inside the Earth, in the Earth’s crust, in the oceans, in the atmosphere, and in us!

It’s worth clicking through to see more detail, like how the heavier elements are more common in us and the Earth than the oceans or air, and how the noble gases on the right of the table are most common in our atmosphere and in space, whereas we and the Earth and the oceans have more of the reactive elements that ionize easily, those in the farthest left and nearly farthest right columns. Also, see how in the periodic table for the universe, the square for hydrogen is nearly black? Hydrogen is by far the most common element in the universe, and making heavier elements requires nuclear fusion in the heart of a star. It’s cool to see visual reminders of that basic fact, that the elements we rely on have all been built by stars.

One of the most intriguing experiences in science is observing something completely counterintuitive. And then having to figure out, okay, why is everything I thought I knew wrong in this case, and what experimental or theoretical studies can I do that will help explain this? That’s the appeal and the challenge of nanoscience: things at a small scale behave very differently from what we’d guess based on observations at a large scale. So how does weirdness inherent in the quantum world come into play?

A single atom has different properties than a bulk material that has trillions of atoms together. That’s because there are a discrete number of possible configurations for the atom to be in, which means discrete energy levels. This is called quantization, as opposed to the continuous smear of available configurations and energy levels that a bulk material has. But if we move away from the extreme cases, where does bulk behavior stop and quantized behavior kick in? Are two atoms still a quantum object? Three? It turns out that quantization of material properties actually persists for awhile, and collections of hundreds or thousands of atoms can still show quantization.

So how do we know where the transition point is between bulk and quantized properties? If we think about shrinking a material down, at some point the size of the material will become smaller than the size of the electronic wavefunction in that bulk material. Below that size, the electrons are “confined” and the states available to them start to change depending on the material size. So we can define a length that is a “quantum confinement limit” for each material. Below the limit, the collection of atoms is confined and has quantum properties, and above the limit it’s approximately the same as a bulk material.

Once we know that limit, there are several ways to make nanomaterials that have quantized properties. We can make nanostructures that are confined in one dimension, like nanosheets, but bulk-like in the other two. We can also make nanowires, which are confined in two dimensions but have one bulk-like dimension. Or, we can make “quantum dots” which are confined in all three dimensions. Quantum dots are like little islands of material, with discrete energy levels just like an atom would have. And one consequence of quantization is that the wavelength of light that quantum dots absorb and emit actually depends on size, as in the image below. Smaller quantum dots absorb and emit bluer light, because the size of the quantum dot increases the spacing between energy levels. There are lots of applications for this effect, such as solar cells whose absorption spectrum is tuned to that of the sun, or LEDs that emit tunably-colored light.

But at the nanoscale, the surface of the object is a lot more important. In something macroscale, like a brick, less than 0.0001% of the atoms are on the surface of the object, but in a quantum dot 30% of the atoms may be surface atoms. That makes surfaces very important! And surface atoms can be the sites of electronic defects, or the sites of bonding by various chemical species that change the properties of the quantum dot. So surface chemistry becomes important, and the quantum dot or nanowire or nanosheet may be very sensitive to small changes in the environment. This can be an asset, though, for example to make gas sensors from chemically functionalized nanomaterials.

Another consideration is that if a material has some features that are nanoscale, those features may be as small as or even smaller than the wavelength of visible light. Practically speaking, this means it’s often easier to image nano-objects with electrons rather than photons. But again, there’s an upside, because you can tune the nanoscale features to interact with light in specific ways or even be hidden from interactions light. This is one of the most interesting things about metamaterials, which I’ll write more about soon!

In our exploration of electronics, we started at the atomic level with the fundamental properties of subatomic particles. We looked at emergent properties of collections of atoms, like the origins of chemical bonding and electronic behavior of materials. Recently we have started to move up in scale, seeing that individualcircuitcomponents affect the flow and storage of electrons in different ways. At this point I think it is worthwhile to take a step back and look at the larger picture. While individual electrons are governed by local interactions that minimize energy, we can figure out global rules for a circuit component that tell us how collections of electrons are affected by a resistor or some other building block, creating the macroscopic quantity we call current. From there we can create collections of circuit components that perform various operations on the current passing through them. These operations can again be combined, and where we may have started with a simple switch, we can end up with a computer or a display or a control circuit.

One way to picture it is like a complex canal system for water: we have a resource whose movement we want to manipulate, to extract physical work and perhaps perform calculations. At a small scale, we can inject dye into a bit of water and watch its progress through the system as it responds to local forces. But we can look at water currents at a larger scale by adding up the behavior of many small amounts of water. In fact, scale is a type of context, a lens through which a system can look quite different! Electrical engineers who design complex circuits for a living tend to work at a much higher level of abstraction than do scientists working on experimental electronic devices. The electrical engineers have to be able to imagine and simulate the function of impressive numbers of transistors, resistors, and other components, as shown below. Whereas a device physicist focuses on the detailed physics in a single circuit component, to learn what its best use might be. They are each working with the same system, but in different and complementary ways.

When I first started writing here, I talked about science as a lens through which we can view the world: a set of perspectives that let us see the things around us in a different way than we are used to. But there are lots of different worldviews and perspectives within science, depending on scale as well as other contexts. A discussion of electrical current, for example, could be handled quite differently depending on whether electrons are moving through a polar solvent like water, or synapses in the brain, or a metal wire connecting a capacitor to an inductor. Scientists who have trained in different fields like physics, chemistry, or biology can imagine very different contexts for discussions of the same phenomenon, so that even when the fundamental science is the same, the narrative and implications may change between contexts.

But in the end, whether you are a scientist or just interested in science, it helps to know not only that an electron is a tiny charged particle, but also how it behaves in electronic circuits, in chemical bonds between atoms, and in biological systems. And to know that it’s possible to build computers out of gears, billiard balls, or even crabs! But the size and properties of electronic computers have led them to dominate, at least for now.

Now that we have looked at the broader picture of what a bond is, we can go a little deeper. Bonds can be easy or hard to break, they can involve particle exchange between atoms, they can be the result of transient forces, and they can react in a variety of ways. There is a rainbow of bond types to explore, but we can focus on a few primary examples.

We’ll start with the stronger sort of bonds: those that involve direct transfer of electrons between atoms. For example, say we have two neighboring atoms, one with an empty low-energy state and one with an outer electron that’s all alone at a high-energy state. If the states are similarly shaped, both atoms can lower their overall energy when the extra electron moves to the low-energy state. The atom that gave up the electron is now positively charged, and the atom that accepted the electron is negatively charged, so there is an electrostatic force attracting them. Charged atoms are also called ions, so we say that these two atoms have an ionic bond. And it’s possible to have ionic bonds involving more than one electron, if an atom has two or three electrons to donate which another atom can accept. A common example of ionic bonding is table salt, which has a sodium atom donate an electron to a chlorine atom.

It’s also possible for two atoms to share a pair of electrons, so that the electron cloud overlaps with both atomic nuclei. If the electrons in question have oppositely aligned spins, they can have the same energy without being in the same quantum mechanical state. This is called covalent bonding. It happens most often when the two atoms in question are comparably attractive to electrons, for example if they are the same type of atom. Graphite, or pencil lead, is one form of carbon that has covalent bonds. So is graphene, the atomically thin version of graphite whose discovery (and extraordinary properties) recently garnered a Nobel prize in physics.

Ionic and covalent bonds tie atoms together very tightly, and can be linked together to form complexes with many bonded atoms. These complexes are known as molecules. But large numbers of atoms can also share electrons diffusely, so that the electrons aren’t localized to a single atom or a pair of atoms. This is called metallic bonding, so-called because delocalized electrons are found in metals. The free electrons move around the atomic nuclei like a sea moving around rocks, only weakly bound to them. The mobility that electrons have in metals is why we say that metals have high ‘electrical conductivity’: it is easy to pass an electrical current, which just consists of individual electrons, through a metal. As a special case of metallic bonding, it’s also possible to have partially delocalized electrons in small molecules, which is the basis of organic chemistry.

Another way to weakly bind atoms comes from the fact that charge is separated in an atom, between the positively charged nucleus and the negatively charged electron cloud. Imagine that the cloud is slightly distorted, by a passing electrical field or by a random fluctuation. If the electron cloud is not symmetric around the nucleus at that moment, there will be a distance between the center of the positive charge and the center of the negative charge, and a force because of the opposite charges. This is called a dipole in electromagnetism, because of the two oppositely charged poles. And if you have two next to each other, they will try to align so that the negative side of one dipole is near the positive side of the other. What starts as a small fluctuation can cause a slight reordering over a large material, because of the dipoles attempting to align. This dipole-dipole interaction is another weak form of bonding. It can happen with induced dipoles, as I’ve described, or between permanent dipoles which are common in molecules.

There is also a lone form of chemical bonding which doesn’t rely solely on electrons. The hydrogen atom, with its single proton and single electron, is pretty small and pretty reactive. So it’s actually possible for two atoms to share a third atom, hydrogen, which means that both the electron and the proton are in energy states that minimize the total system energy. The hydrogen bond is partly covalent, since the hydrogen electron is usually paired with a second electron. But the separation of the proton and electron also induces a dipole, making hydrogen bonding a dipole-dipole interaction. Hydrogen bonding may sound like a strange beast, and it is, but it is an important factor in the chemical behavior of water which is essential to life as we know it.

Learning the structure and mechanism behind everyday life is one of the things that drew me to science. And there are few better examples of that than cooking, an activity which is pretty necessary and central to life! The way that cooking is taught actually shares a lot with the way that science is taught. Initially you memorize recipes, formulae, and techniques without necessarily having a clear idea of the motivations. But as you gain skill you learn more about the fundamentals and the why of what is happening! In science the fundamentals can be things like the basic forces, atomic interactions, or the use of math to unify behavior at many different size scales. And in cooking, as you search for motivation you begin delving into chemical reactions, mechanical processes that modify ingredients, and the biology of the things being eaten as well as the person doing the eating.

There are a lot of excellent books on this out there, notably On Food and Cooking by Harold McGee. But there’s also a nice online resource, lectures from a popular Harvard course on science and cooking. Each week they invited a guest chef to give a public talk, and do a course lecture and demonstration. Then they had a lecture from the course organizers to go into a specific scientific concept in the guest chef’s demo. And finally, they went into a lab to recreate the dish shown or another dish that built on the same scientific concept. The full list of lectures, covering things like phase changes, browning, emulsions, viscosity, and heat, is available here, and here is the first lecture:

The structure of the periodic table of elements is a bit weird the first time you see it, like a castle or a cake. If we just read the periodic table top to bottom and left to right, we are reading off the elements in order of increasing number of protons. However, if this were the only useful ordering on the periodic table, it could be a simple list. The vertically aligned groups on the periodic table actually represent the chemical properties of the elements. Dmitri Mendeleev developed the table in 1869 as a way to both tabulate existing empirical results, and predict what unexplored chemical reactions or undiscovered elements might be possible. It was revolutionary as a scientific tool, but the mechanism behind the periodicity was not understood until decades later. As it turns out, the periodicity of chemical behavior corresponds to the bonding type of the outer electrons in different atoms.

To understand what that means, we can start by looking at the elements on the left side of the periodic table. Hydrogen has only one proton, so the electrically neutral form of hydrogen has only one electron. This single electron is a point particle, jumping around the nucleus. The electron exists in a probability cloud, whose shape is given by the lowest energy solution to the quantum mechanical equations describing the system. These quantum states can be distinguished by differing quantum numbers for various quantities like spin and angular momentum, and we will talk about these in more depth later on. When we add additional electrons, they all want to be in the lowest energy state as well. Sadly for electrons but happily for us, no two electrons are able to occupy the same quantum state: they must differ in at least one quantum number. This is known as the Pauli exclusion principle, and was devised to explain experimental results in the early years of quantum mechanics. So while the single electron in hydrogen gets to be in the lowest energy state available for an electron in that atom, in an atom like oxygen, its eight electrons occupy the eight lowest energy states, as if they are stones stacked in a bucket.

But what’s really interesting about these higher energy electron states is that they have different shapes, as we can see by the mathematical forms that describe the possible probability distributions for electrons. So while the electron cloud in a hydrogen atom is a sphere, there are electron clouds for other atoms that are shaped like dumbbells, spheres cut in two, alternating spherical shells, and lots of other shapes.

The electron cloud shape becomes important because two atoms near each other may be able to minimize their overall energy via electron interactions: in some configurations the sharing of one, two, more, or even a partial number of electrons is energetically preferred, whereas in other configurations sharing electrons is not favorable. This electron sharing, which changes the shape of the electron cloud and affects the chemical reactivity of the atoms involved, is what’s called chemical bonding. When atoms are connected by a chemical bond, there is an energy cost necessary to separate them. But how atoms interact depends fundamentally on the shape of the electron cloud, determining when atoms can or can’t bond to each other. So the periodic table, which was originally developed to group atoms with similar chemical properties and bonding behaviors, actually also groups atoms by the number and arrangement of electrons.

Now, there is a lot more that can be said about bonding. You can talk about the inherent spin of electrons, which is important in bonding and atomic orbital filling, or you can talk about the idea of filled electron shells which make some atoms stable and others reactive, or you can talk about the many kinds of chemical bonds. It’s a very deep topic, and this is just the beginning!

Since every real world object is a collection of bonded atoms, the properties of the things we interact with, and what materials are even able to exist in our world, depend on the shape of the electron cloud. Imagine if the Pauli exclusion principle were not true, and all the electrons in an atom could sit together in the lowest energy state. This would make every electron cloud the same shape, which would remove the incredible variety of chemical bonds in our world, homogenizing material properties. Chemistry would be a lot easier to learn but a lot less interesting, and atomic physics would be completely solved. Stars, planets, and life as we know it might not exist at all.